# Mathematics Grade 10 Paper 1 KZN June 2024 Memo > Grade 10 Mathematics Paper 1 memorandum from the KZN June Exam 2024, 10 pages. Read online or get the free PDF download, question paper linked when available. - Page: https://www.hlayiso.com/library/kzn-maths-grade-10-june-2024-p1-and-memo/8da9eb20-3c87-421a-81c6-de9f36a4d302 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 10 - Document type: Memorandum - Year: 2024 - Exam period: KZN June Exam - Paper: 1 - Curriculum: CAPS - Pages: 10 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 10](https://www.hlayiso.com/library/grade-10) › [Mathematics](https://www.hlayiso.com/library/grade-10/mathematics) › [Mathematics Grade 10 Paper 1 KZN June 2024 Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-june-2024-p1-and-memo/8da9eb20-3c87-421a-81c6-de9f36a4d302) ## About this document Mathematics · Grade 10 · KZN June Exam · 2024. Memorandum, 10 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com Downloaded f rom St anmorephysics. com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 COMMON TEST JUNE 2024 MARKS: 50 TIME: 1 hour This question paper consists of 5 pages. Copyright Reserved Please Turn Over ### Page 2 Downloaded from hlayiso.com Mathematics P1 2 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 3 questions. 2. Answer ALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 5. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Write neatly and legibly. Copyright Reserved Please Turn Over ### Page 3 Downloaded from hlayiso.com Mathematics P1 3 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 1 1.1 Simplify fully: 1.1.1 ( 3x − 2 ) ( 2 x 2 − 4 x + 1) (2) 1.1.2 4 x.8 x +1 32 x +1 (3) 1.1.3 x+7 3 2 − + x −x − 6 x − 3 2x + 4 2 (5) 1.2 Factorise fully: 1.2.1 5x2 − 2 x − 3 (2) 1 1.2.2 x3 + 125 (2) [14] QUESTION 2 2.1 Solve for x: 2.1.1 x ( x − 1) = 6 (3) 2.1.2 3x + 3x−1 = 36 (3) x 2.1.3 −2  −1  1 3 (3) 2.2 A shop sells bicycles and tricycles. In total there are 7 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two (5) wheels and a tricycle has three wheels. [14] Copyright Reserved Please Turn Over ### Page 4 Downloaded from hlayiso.com Mathematics P1 4 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 3 3 3.1 Given: f ( x ) = x − 2 and g ( x ) = , which are not drawn to scale. A and B are points of x intersection of the graphs. DF is perpendicular to the x-axis, with points E and F on the graphs of g and f respectively. Determine: 3.1.1 The coordinates of point C. (1) 3.1.2 The x-coordinates of A and B. (4) 3.1.3 The length of EF if OD = 6 units . (3) 3.1.4 The equation of j if j ( x ) = g ( x ) + 2 . (1) 3.1.5 The value(s) of x for which f ( x )  g ( x ) where x  0 . (2) Copyright Reserved Please Turn Over ### Page 5 Downloaded from hlayiso.com Mathematics P1 5 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com 3.2 Sketch the graph of h( x) = ax 2 + q if it is given that: • The range of h is  −4;  ) • a0;a0 • q0 • One root of h is positive and one root of h is negative. (3) 3.3 Given: g ( x ) = 3.2x − 12 3.3.1 Write down the equation of the asymptote of g . (1) 3.3.2 Determine the y intercept of g . (2) 3.3.3 Determine the x intercept of g . (2) 3.3.4 Sketch the graph of g, clearly showing the asymptote and the intercepts with the (3) axes. [22] TOTAL: [50] Copyright Reserved Please Turn Over ### Page 6 Downloaded from hlayiso.com Downloaded f rom St anmorephysics. com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 COMMON TEST JUNE 2024 MARKING GUIDELINE MARKS: 50 This marking guideline consists of 5 pages. Copyright Reserved Please Turn Over ### Page 7 Downloaded from hlayiso.com Mathematics 2 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 1 1.1.1  6 x3  12 x 2  3x  4 x 2  8 x  2 Asimplification  6 x3  16 x 2  11x  2 CAanswer (2) 1.1.2 2 2 x.23 x 3 22 x.23 x 3  A 25 x  5 25 x  5  2 2 CA 22 1 1 (3)  CA 4 4 1.1.3 x7 3 2 A  x  3 x  2  and 2(𝑥 + 2)     x  3 x  2  x  3 2  x  2  x  7  3 x  2  x  3 CA x  7  3 x  2  x  3  x  3 x  2   x  3 x  2  x  7  3x  6  x  3   x  3 x  2  CA  x  2 x  2   x  3 x  2  CA   x  2    x  2   x  3 x  2  1 1 CA  x3 x3 (5) 1.2.1   5 x  3 x  1 A  5 x  3 A  x  1 (2) 1.2.2  1  1 1   1   x    x2  x   A  x    5  5 25   5  1 1  A  x 2  x   (2)  5 25  [14] Copyright Reserved Please turn over ### Page 8 Downloaded from hlayiso.com Mathematics 3 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 2 2.1.1 x2  x  6  0 Astandard form CAfactors  x  3 x  2   0 x  3 or x  2 CAboth answers (3) 2.1.2  1  1 3x  1    36 A 3x  1    36  3  3 3  27 x CA 3x  27 x3 CA x  3 (3) 2.1.3 x x 2  1   11 A 2  1   11 3 3 x x 1  2 CA 1  2 3 3 (3) 3  x  6 CA 3  x  6 2.2 Let bicycles  x tricycles  y x  y  7.............  (1) A x  y  7 2 x  3 y  19.........  (2) A 2 x  3 y  19 2 x  2 y  14......  (3) CA 2x  2 y  14 Add (2) and (3) y 5 CA y  5 x2 CA x  2 OR x  y  7.............  (1) 2 x  3 y  19.........  (2) OR A x  y  7 x  7  y..............  (3) A 2 x  3 y  19 subst. (3) into (2) CA x  7  y 2  7  y   3 y  19 14  2 y  3 y  19 y5 CA y  5 x2 (5) CA x  2 [14] Copyright Reserved Please turn over ### Page 9 Downloaded from hlayiso.com Mathematics 4 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 3 3.1.1 f  0   2 A C  0; 2  C  0; 2  (1) 3.1.2 3 3 x2 A x  2  x x x  2x  3  0 2 A x  2 x  3  0 2  x  3 x  1  0 CA  x  3 x  1  0 x  3 or x  1 CA x  3 or x  1 A  1; 0  , B  3; 0  (4) 3.1.3 f  6  6  2 A y – value of F 4 3 g 6  6 1 A y – value of E  2 7 7  EF=3,5 or units CA EF=3,5 or units 2 2 (3) 3.1.4 3 3 j ( x)  2 A j ( x)  2 (1) x x 3.1.5 1  x  0 CA 1  x  0 A OR x [1;0) (2) Copyright Reserved Please turn over ### Page 10 Downloaded from hlayiso.com Mathematics 5 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline 3.2 Ashape Ax-intercepts on either sides of the y- axis Aturning point /y- intercept at y  4 (3) 3.3.1 y  12 Aanswer (1) 3.3.2 g  0   9 A g (0)  3.20 12 A 9 (2) 3.3.3 3.2 x  12 A 2 x  4 2x  4 A x  2 (2) x2 3.3.4 Ashape CAboth intercepts Aasymptotes (3) [22] TOTAL: [50] Copyright Reserved Please turn over ## Related documents - [Gr 10 Mathematics P1 (Afrikaans) June 2024 Question Paper](https://www.hlayiso.com/library/gr-10-mathematics-p1-afrikaans-june-2024-question-paper/f7a97f78-e0a1-47a0-9585-d048fbb9a0b0) — Mathematics · QP · 2024 · Afr - [Gr 10 Mathematics P1 (English) June 2024 Question Paper](https://www.hlayiso.com/library/gr-10-mathematics-p1-english-june-2024-question-paper/f3793ce3-e07c-4539-b525-ae281a304900) — Mathematics · QP · 2024 · Eng - [KZN Maths Grade 10 November 2024 P1 and Memo](https://www.hlayiso.com/library/grade-10-mathematics-2024-kzn-november-exam-question-paper-and-memorandum-paper-1/537eaec3-454e-4215-b0ac-1120ed68430a) — Mathematics · QP + Memo · 2024 - [GR10 MATHEMATICS P1 QP AFR](https://www.hlayiso.com/library/grade-10-mathematics-2024-north-west-november-exam-question-paper-paper-1-afrikaans/6037af3f-6a37-4c7d-ba44-b668ace90d90) — Mathematics · QP · 2024 · Afr - [KZN Maths Grade 10 June 2025 P1 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-june-2025-p1-and-memo/dc5ae33f-46ec-4eae-b577-25a82956eaec) — Mathematics · QP + Memo · 2025 - [Gr 10 Mathematics P1 (English and Afrikaans) November 2022 Possible Answers](https://www.hlayiso.com/library/gr-10-mathematics-p1-english-and-afrikaans-november-2022-possible-answers/95c1561e-9f52-43c1-82af-15858ae5bc23) — Mathematics · Memo · 2022 · Afr ## More from Grade 10 Mathematics - [Gr 10 Maths ATP 2023-24](https://www.hlayiso.com/library/gr-10-maths-atp-2023-24/80c1c337-e011-4b8b-a37b-d2e0df9daaf6) — ATP - [KZN Maths Grade 10 March 2025 QP and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-march-2025-qp-and-memo/bc27cbbf-ec6d-4c60-bf7e-25a154d363e4) — QP + Memo · 2025 - [KZN Maths Grade 10 November 2025 P1 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-november-2025-p1-and-memo/ece9abee-2009-4e22-8de3-34ccb229e5cb) — QP + Memo · 2025 - [KZN Maths Grade 10 November 2025 P2 and Memo](https://www.hlayiso.com/library/kzn-maths-grade-10-november-2025-p2-and-memo/417e9b18-c39d-4fb2-9e32-c089e8fbfd22) — QP + Memo · 2025 - [Gr 10 Mathematics P2 (Afrikaans) June 2024 Question Paper](https://www.hlayiso.com/library/gr-10-mathematics-p2-afrikaans-june-2024-question-paper/0746972c-d0cc-4ba2-bcc7-f65ad2bdf324) — QP · 2024 · Afr - [Gr 10 Mathematics P2 (English) June 2024 Question Paper](https://www.hlayiso.com/library/gr-10-mathematics-p2-english-june-2024-question-paper/b92d4e62-fb6d-4b45-9798-0ce101056196) — QP · 2024 · Eng ## Collection - [Grade 10 past papers](https://www.hlayiso.com/grade-10/past-papers) --- Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. 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